Glass-like behavior of a hard-disk fluid confined to a narrow channel

TL;DR

This study investigates glass-like dynamics in a confined hard-disk fluid, revealing caging behavior and structural features linked to glass transition phenomena through simulations and exact structural analysis.

Contribution

It introduces a detailed analysis of caging and dynamical length scales in a narrow channel hard-disk system, connecting static structural features with dynamical slowing down.

Findings

Dynamical length scale grows with time and correlates with static zigzag order.

Caging behavior emerges at a characteristic packing fraction $_d$.

Structural features related to glassy behavior are identified in the structure factor.

Abstract

Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks which sets in at characteristic packing fraction $\phi_d$. Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event driven molecular dynamics simulations and the time dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above $\phi_d$. The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer matrix approach.